High-fidelity numerical simulations and their impact on the research and development of detonation-based, pressure-gain combustion devices are discussed in this paper. Both time-dependent one- and multidimensional simulations have been used to highlight the advantages and limitations of these approaches. The level of fidelity of the physical models is established by comparison to experimental data. The results of detailed, one-dimensional numerical simulations are generalized to identify three key factors that control the idealized performance of a pulse detonation engine device. Multidimensional detonation structure studies are used to explain the observed difficulty in the initiation and transmission of detonations in ethylene–air mixtures in pulse detonation engine devices. Then multidimensional simulations of rotating detonation engine device are used to describe the basic flow field within such a device. The key parameters that control the idealized performance of these devices are explored using the simulations. The effect of injection and exhaust geometry is also highlighted.